Java Recursion Slides provided by the University of Washington - - PowerPoint PPT Presentation

Java Recursion

Slides provided by the University of Washington Computer Science & Engineering department. Adapted from slides by Marty Stepp, Stuart Reges & Allison Obourn.

• recursion: The definition of an operation in terms of itself
• Solving a problem using recursion depends on solving

smaller occurrences of the same problem.

• recursive programming: Writing methods that call

themselves to solve problems recursively

• An equally powerful substitute for iteration (like for-

loops)

• Particularly well-suited for solving certain types of

problems

Recursion

Recursion and cases

• Every recursive algorithm involves at least 2 cases:
• base case: A simple occurrence that can be answered

directly

• recursive case: A more complex occurrence of the

problem that cannot be directly answered, but can instead be described in terms of smaller occurrences of the same problem

• Some recursive algorithms have more than one base or

recursive case, but all have at least one of each.

• A crucial part of recursive programming is identifying these

cases.

Recursion in Java

• Consider the following method to print a line of * characters:

// Prints a line containing the given number of stars. // Precondition: n >= 0 public static void printStars(int n) { for (int i = 0; i < n; i++) { System.out.print("*"); } System.out.println(); // end the line of output }

• Write a recursive version of this method that calls itself.
• Solve the problem without using any loops.
• Hint: your solution should print just one star at a time.

Recursion in Java

• Our recursive solution is split into two cases:
• base case: print 0 stars
• recursive case: print more than 0 stars
• In Java:

public static void printStars(int n) { if (n == 0) { // base case; just end the line of output System.out.println(); } else { // recursive case; print one zero stars System.out.print("*"); printStars(n - 1); } }

Recursive tracing

• Consider the following recursive method:

public static int mystery(int n) { if (n < 10) { return n; } else { int a = n / 10; int b = n % 10; return mystery(a + b); } }

• What is the result of the following call?

mystery(648)

A recursive trace

mystery(648):

• int a = 648 / 10; // 64
• int b = 648 % 10; // 8
• return mystery(a + b); // mystery(72)

mystery(72):

• int a = 72 / 10; // 7
• int b = 72 % 10; // 2
• return mystery(a + b); // mystery(9)

mystery(9):

• return 9;

Recursive tracing 2

• Consider the following recursive method:

public static int mystery(int n) { if (n < 10) { return (10 * n) + n; } else { int a = mystery(n / 10); int b = mystery(n % 10); return (100 * a) + b; } }

• What is the result of the following call?

mystery(348)

A recursive trace 2

mystery(348):

• int a = mystery(34);
• int a = mystery(3);
• return (10 * 3) + 3; // 33
• int b = mystery(4);
• return (10 * 4) + 4; // 44
• return (100 * 33) + 44; // 3344
• int b = mystery(8);
• return (10 * 8) + 8; // 88
• return (100 * 3344) + 88; // 334488